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Let's say I have a bucket of aqueous solution, and it

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contains some weak acid in it.

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And so weak acid.

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We've done this multiple times.

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It's in equilibrium with its dissociated state.

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So it would be in equilibrium.

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Let me write the aqueous.

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So it's a weak acid, where the A could be any other kind of

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molecular group.

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That could be the conjugate base of the weak acid.

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So that's in equilibrium with some hydrogen ions, so it'll

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produce some of them, but some of this is going to

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be around as well.

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Plus its conjugate base.

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A minus.

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Aqueous.

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And just like we did with the strong acid titration, let's

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measure it's pH.

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So I'll do that right here.

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Actually, I want to do it a little higher.

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So let's do it right there.

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Let me make a little scale here.

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So this is 0.

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Let's say that right there is 7.

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That this right here is 14.

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So our first measurement of the pH of our solution-- we

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have a maybe a liter of it.

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Let's say we have 1 liter of our solution.

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We don't know the concentration of this thing.

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But let's say our first measurement, we go and we say

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OK, it's got a pH of-- I don't know.

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Something here.

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Let's say it's got a pH of 3.

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So it's acidic, not ultra acidic, but it's acidic.

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So it's got a pH of 3 right there.

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This whole scale on the left-hand side.

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This is all pH, just like in the last video.

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This is pH.

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The pH is going up as you go up the scale.

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That's our first measurement.

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Now we're going to titrate this weak acid, just like we

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titrated the strong base.

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And normally when you do this-- I mean, you can, in

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theory, titrate with anything.

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But you normally titrate-- if you're titrating an acid,

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whether it's weak or strong-- you always titrate with a

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strong base.

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And if you are titrating a base, whether it's weaker

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strong, the reagent, or the thing that you're going to

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add, is going to be a strong acid.

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So in this case, even though we're going to drop some drops

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into a weak acid, we're going to drop

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drops of a strong base.

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So let's use sodium hydroxide again.

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NaOH.

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And just to make things interesting, to make the math

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a little interesting, let's say it's a 0.5 molar solution.

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And we're going to add it in increments of little

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100-milliliter increments.

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A tenth of a liter.

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But the interesting thing is really the shape of the curve

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that forms, or the titration curve, or the pH curve.

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Let me write what the reaction of NaOH.

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Just so you have that in your head.

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NaOH, sodium hydroxide, and I did this in

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the previous video.

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It disassociates completely in water.

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And so it turns into Na plus-- all this is aqueous, of

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course-- plus OH minus.

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So when you throw even a little bit.

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Let's say you throw in-- this is 0.5 molar solution-- 100

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milliliters.

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That's equal to one tenth of a liter.

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This 0.5 molar, that's its molarity.

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So it says hey, I'm going to have half a

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mole of this stuff.

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Or really, of this stuff.

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I'm going to have half a mole of hydroxide

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ions for every liter.

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So in one tenth of a liter, that means that I'm

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going to have what?

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I'm going to have half of that.

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So I'm going have 1/20, or 0.05 moles.

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So let's say this point right here's is 100 milliliters.

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I've added 100 milliliters of our solution.

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That's going to have 0.5 moles of OH.

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Because remember, we could say it's 0.5 moles of this, but

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whenever this is in solution, it disassociates

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completely into this.

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So if you have 0.5 moles of this, you really have 0.5

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moles of this.

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This will be in this form completely, because it's a

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strong base.

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So if I have 0.5 moles of this and I throw it into the

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solution, what's it going to do?

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It's going to start sopping up some of our hydrogen ions.

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So it's going to increase the pH, and it's going to keep

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increasing.

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Right?

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And this is a buffer.

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And this is a key thing to remember.

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This is going to sop some of this thing up.

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But this is a buffer.

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This is a weak acid.

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So it's in equilibrium.

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So it has this reserve over here of the acid form.

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So when you start lowering this by adding a strong base

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to it, to sop this up, what's going to happen?

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The reaction is going to move in this direction to kind of

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backfill, to fill or to almost replace.

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It won't get quite to where it was before, but it's going to

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dampen the stress on the equilibrium.

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So what's going to happen is the concentration of your weak

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acid is going to go down.

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It's going to try to backfill this stuff.

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But every time the reaction goes in this direction, this

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is going to go up.

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Right?

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Remember, nothing is sopping up the conjugate

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base up here, right?

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We're just sopping up the hydrogen ions.

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As we sop up more and more hydrogen ions, this reaction

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goes more and more in the rightward direction.

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But as it goes more and more in the rightward direction,

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we're just adding more and more to this.

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And the base just takes more and more of this out.

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So essentially when the base is taking this out, it's

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really taking this out-- or it's taking half of this out.

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It's taking the H part of this out.

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Because that converts to that, and it gets sopped up by the

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by the reagent.

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The strong base.

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And all of this ends up on this side, as

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the conjugate base.

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So at some point, when we have added the exact same amount of

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OH as there is of this stuff, as there is of this stuff plus

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the hydrogen.

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When we've sopped up all of the hydrogen,

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what's going to happen?

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Well, right when you get above that point, when you start

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adding even more, you're going to start getting very basic.

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It's just going to skyrocket up the pH.

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Because then you're adding OHs, and they're not being

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canceled out by any hydrogen over there.

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And there's nothing to kind of backfill the hydrogen.

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So you're going to get to a very high reaction.

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When we add enough of the sodium hydroxide that this

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completely neutralizes this and this, and all we

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have left is that.

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Well, you might say, oh, we have a pH of 7 because all of

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the acid is neutralized.

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But we don't have a pH of 7 like we did with the strong

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base, because here, as we sopped up stuff, we kept

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adding conjugate base over here.

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Remember, and it's a real base.

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It actually has basic properties.

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If this is a strong acid, if this was hydrogen chloride,

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I'd still have the chloride over here.

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But chloride, even though it's the conjugate base, it has no

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basic properties.

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It does not increase the pH of a solution.

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But this stuff right here does increase the pH of a solution.

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And we've done that in previous videos.

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So once all of this is sopped up, your equivalence point, or

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the point at which the number of moles of this is equal to

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the number of moles of this, is going to have a high pH.

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So it's going to be like right over there.

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And then as you add more and more of your reagent, or your

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strong base, your pH is going to get higher and higher and

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approach 14 or even go above it.

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So your titration curve is going look

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something like this.

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And once again, you look at the steepest

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point on the curve.

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It's right there.

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And you say, OK, that's the equivalence point.

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That's the point at which I had an equal amount of

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hydroxide having sopped up all of the hydrogen, and I've run

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out of all of this stuff to backfill the hydrogen.

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So you look at your equivalence point.

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And you say, OK, if that equivalence point was when I

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added, I don't know.

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Maybe that's when you added 2 liters of your reagent.

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So you added 2 liters of your reagent.

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Your basic reagent, right here.

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Or your titrant.

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Or titrator.

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I think that's another word for it.

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How many moles have you added?

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Well it's 2 liters, it's 0.5 molar, so you've added 1 mole.

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So here you've added 1 mole of OH.

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And when you added 1 mole of OH, you sopped up all of the

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whatever mole you had of this.

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So you clearly had 1 mole of that.

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So over here, your original concentration of your-- I

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mean, you really could say your concentration of your HA

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plus your initial equilibrium hydrogen is equal to 1 molar.

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Now in most chemistry classes, this number is way bigger than

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this number for most weak acids.

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And you could look at that.

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Because if you look at some of the pKa's for some weak acids,

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you'll see that this is some-- well, I won't go into the

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math, but this number's a lot lower.

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So this is an indication, essentially, of your initial

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concentration of your weak acid.

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So you essentially just keep titrating it, figure out the

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inflection point, you say, the inflection point happened when

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I added 2 liters of the titrator to it, which

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corresponded to 1 mole.

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So therefore I must have had 1 mole of my original acid in

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the equation.

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Another interesting thing.

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So if you said OK, I had 1 mole of my original acid in

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the equation.

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So you say, this was 1 molar originally, before I started

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titrating it all.

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And if I said that this is a 1 liter solution-- this is 1

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mole, not 1 molar.

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But if I know it's a 1-liter solution, now I know that

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originally I had 1 mole in 1 liter, so I had

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a molarity of 1.

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Now, let me go over something else that's interesting about

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a basic reaction.

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Actually, let me do that in the next video, because I

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think this one's getting a little long.